210 pso its eng apps

8/3/2019 210 Pso Its Eng Apps

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Particle Swarm Optimization:Recent Advances and Applications

Dr. Voratas Kachitvichyanukul Asian Institute of Technology

August 24, 2007TGCC 2007 Conference

THAILAND


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Research Team Members

The Jin Ai Pisut Pongchairerks Thongchai Pratchayaborirak Vu Xuan Troung Voratas Kachitvichyanukul


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Outline

Classical PSO Pitfalls of PSO Design Considerations Recent PSO extensions Applications of PSO Multi-objective Job shop scheduling Capacitated Vehicle Routing Multimode Resource Constrained Project

Scheduling

Summary


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Separation : steer toavoid crowding localflockmates

Alignment : steer towardsthe average heading oflocal flockmates

Cohesion : steer to movetoward the average positionof local flockmates

Mimicking nature!!!


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Introduction

Developed by Kennedy and Eberhart in1995.

The motivation of PSO algorithm was

social behavior such as bird flocking, andfish schooling.

PSO is a population-based method, like

Genetic algorithm. However, the basicconcept is cooperation instead of rivalry.


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PSO features

PSO is very similar to GA, but it doesnot have genetic operators (crossoverand mutation).

A particle moves with the velocity: its own experience, experience from all particles.

The idea is similar to bird flockssearching for food.


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PSO Demo


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Properties of Particles

1. ability to exchange information withits neighbors

2. ability to memorize a previousposition

3. ability to use information to make a

decision.


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Inertia Term:- This term forces the

particle to move in thesame direction

- Audacious tendency,following own wayusing old velocity

VELOCITY UPDATI

3 terms that create new velocity:

1. Inertia Term

2. Cognitive Term

3. Social Learning Term


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Cognitive Term:(Personal Best)This term forces theparticle to go back tothe previous bestposition: Conservativetendency

Velocity Updating


1. Inertia Term

2. Cognitive Term



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ar c e warm p m za on~ Basic Idea: Cognitive Behavior ~

An individual remembers its past knowledge

Food : 100

Food : 80Food : 50

Where shouldI move to?


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Social Term:This term forces theparticle to move to thebest previous positionof its neighbors- Sheep like tendency,be a follower

Velocity Updating


1. Inertia Term

2. Cognitive Term



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ar c e warm p m za on~ Basic Idea: Social Behavior ~

An individual gains knowledgefrom other population member

Bird 2Food : 100

Bird 3Food : 100Bird 1

Food : 150

Bird 4Food : 400

Whereshould I

move to?


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vid= v id

+ c 1*r()*(pid

xid)+ c 2*r()*(pgd xid)

vid = [ - V max , Vmax ]

xid = x id + v id

Traditional PSO Eberhart, R. C. and Kennedy, J. (1995)

Update of Velocity & Position

Inertia

Cognitive learning

Social learning

Update Position


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Key Variables

vid velocity of dimension d of the i th particle

p id best previous position of the i th particlepgd is the best position of the neighborsxid current position of the i th particlec

1& c

2are acceleration constants

r() random function in the range [0, 1]w Inertia weight


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PSO algorithm

Initialize particles with random positionand zero velocity

Evaluate fitness value

Compare & update fitness valuewith pbest and gbest

Meet stoppingcriterion?

Update velocity andposition

Start

End

YES

NO

pbest = the bestsolution (fitness)a particle hasachieved so far.

gbest = theglobal bestsolution of allparticles.


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1

2

3

Minimization Problem

Best ParticleOther Particle

1. Initializing Position

2. Create Velocity (Vector)

First Iteration


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1

Minimization Problem

Best ParticleOther Particle

1. Update New Position

2. Create Velocity (Vector)

Second Iteration

1

2

3


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Learning Structures

Inertia Term


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Personal Best (Pbest)

Current Position (X)

Personal Best (Pbest)

Learning Structures


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Current Position (X)Personal Best (Pbest)Global Best (Gbest)

Learning Structures

Global Best (Gbest)


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Pitfalls of PSO

Particles tend to cluster, i.e., converge toofast and get stuck at local optimum

Movement of particle carried it into infeasible

region Inappropriate mapping of particle space into

solution space


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Problem: Particles tend to cluster in the same area. Itreduces movement of swarm as the particles are trapped

in a small local area.


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To solve this problem, some particles can be reinitializedinto new positions which may be in a better area. Other

particles will be pulled to the new area

!


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ModifiedPSO algorithmInitialize particles withrandom position and zero

velocity

Evaluate fitness value

Meet localsearch

criterion?

Compare/update fitnessvalue with pbest and gbest

Meet stoppingcriterion?

Update velocity andposition

Meet re-initialization

criterion?

Start

End

Localsearch

Re-initialization

YES

YES

YES

NO

NO

NO


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Design Considerations

Mapping of particle to solution Number of dimensions Fitness function Number of particles Structure for social learning Values of parameters (c 1 & c 2 etc.) How to handle infeasible particles Stopping criteria


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Example: Random Key for JSP

0.37 0.51 0.81 0.64 0.26 0.13 0.44 0.95 0.83

0.13 0.26 0.44 0.37 0.64 0.51 0.81 0.95 0.83

1 2 3 4 5 6 7 8 9

Particle

Particle Dimension

Dimension 5 6 1 7 2 3 4 8 9

Job 1 1 1 2 2 2 3 3 3

0.37 0.51 0.81 0.64 0.26 0.13 0.44 0.95 0.83 Particle Dimension 1 2 3 4 5 6 7 8 9

Job 1 2 2 3 1 1 2 3 3


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Decoding into solution

0.37 0.51 0.81 0.64 0.26 0.13 0.44 0.95 0.83 Particle Dimension 1 2 3 4 5 6 7 8 9

Job 1 2 2 3 1 1 2 3 3

MC1

MC2

MC3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 time

O jim O111 O213 O221 O313 O122 O133 O232 O322 O331

J1 J2

J1

J2 J3

J2

J1

J3

J3


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Main Components

Intensification is the exploitation of thesolutions found in previous searches

Diversification is the exploration of the

unvisited regions BALANCE !Exploitation Exploration

Quickly identify regionwith potentially highquality solution(s)

Quickly find the bestsolution(s) with in a

region


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Current Research

PSO with multiple social learning terms Measurement Indices for PSO Heterogeneous Particles Hierarchical PSO PSO for Job shop Scheduling Problem PSO for Vehicle Routing Problem PSO for Multimode Resource Constraint

Project scheduling problem


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GLN-PSO

Pongchairerks, P. and Kachitvichyanukul, V. A Non-Homogenous Particle Swarm

Optimization with Multiple Social Structures,Proceedings of the International Conferenceon Simulation and Modeling 2005, Bangkok,Thailand, January 2005.

Particle Swarm Optimization with Multiple

Social Structures, Proceedings of theInternational Computers and IndustrialEngineering Conference, Taipei, Taiwan,June 2006.


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The combination vector created by pbest,gbest, lbest, and nbest pulls each particleto a better direction than previouspublished versions

pbest

gbest

Standard PSOpbest

gbest

nbest lbest

GLN-PSO

More goodinformation sources,

Better performance

GLN-PSO

M I di f PSO


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Measurement Indices for PSO

Two measurement indices aredefined for observing the dynamicbehavior of the swarm.

dispersion index. Velocity index

Need to be embedded in the PSOcode

Will slow down the algorithm

Di i i d


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Dispersion index

It measures how particles are spreadingaround the best particle in the swarm,and is defined as the average absolute

distance of each dimension from thebest particle. It explains the coverage searching area

of the swarm. A swarm with higherdispersion index has relatively widercoverage of searching area than the onewith lower dispersion index.

V l i i d


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Velocity index

It measures how fast the swarm movesin certain iteration, and is defined as theaverage of absolute velocity.

It shows the moving behavior of theswarm: higher index means the swarmmove more aggressively in movingthrough the problem space than theswarm with lower index.

F l


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Formula

Reference:

Ai, T. J., and Kachitvichyanukul, V.,Dispersion and Velocity Indices for Observing

Dynamic Behavior of Particle SwarmOptimization, IEEE Congress onEvolutionary Computation, Singapore,September 2007

1 1

I D

id gd i d

x p

I D 1 1

I D

id

i d

v

I D

Hi hi l PSO


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Hierarchical PSO

Multi-swarm, same parameters, sameobjective Multi-swarm, same parameters,

different objective for each swarm Multi-level, particles in each level may

have different characteristic Easily parallelized Not useful for small problems

Use multi-level as parameter tuningmechanism


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Stage 1: Swarm evolve with percent migration

Stage 2: Initial last swarm by randomly migrate the

evolved particles from all swarms in Stage 1

20%migrate

20 %migrate

End

25% 25 % 25 % 25 %

20%migrate

Swarm 1 Swarm 2 Swarm 3 Swarm 4

Last Swarm

Start

80% NewParticles

80% NewParticles

80% NewParticles

100 % NewParticles

P t ti l A li ti


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Potential Applications

Multi-objective optimization Each swarm may use different objective

function Specialized swarm then combined for a final

search on the overall objective Parallel execution of swarm on clusterPratchayaborirak, T., and Kachitvichyanukul, V.

A Two-Stage Particle Swarm Optimization for Multi-Objective Job Shop Scheduling Problems,Proceedings of the APIEMS 2007 Conference,Taiwan, December 2007

T l l PSO


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Two-level PSO

Top level particle represents PSOparameters to be used in the secondlevel

Second level particle represents problemdomain of interest Eliminate the need for parameter tuning

P t T i g PSO


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Parameter Tuning PSO

Motivations Parameters of PSO are problem specific Generally, factorial experiments are

required to find good parametervalues

Main ideas Use particles to represent parameter

values and use PSO to search for goodparameter values

T L l PSO


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Two-Level PSO

At least two levels of PSO with differentparticles are needed. The top level swarm is used as the

parameters of the bottom level PSO. The bottom level swarm is used to

evaluate the fitness of the particle from

top level swarm.

PT PSO Description (1)


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PT-PSO Description (1)

Level-1 swarm consists of k particle,each particle represents PSO parametersof Level-2 swarm

Level-2 starts with k identical swarms of particles that can be mapped intoproblem solutions.

Each level-2 swarm is paired with alevel-1 particle and each is evolvedunder same conditions.

PT PSO Description (2)


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PT-PSO Description (2)

When level-2 swarm terminated, the bestsolution of the swarm becomes the fitnessvalue of the corresponding level-1 particle

After the fitness values for all level-1 particlesare computed, the velocities and positions of all level-1 particles are updated and the stepsrepeat until the stopping criterion is met

The level-1 particle with best fitness valuebecome the parameter set for the problem


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Job shop scheduling problem(completed)Pongchairerks, P. and Kachitvichyanukul, V.

A Two-level Particle Swarm Optimization Algorithm on Job-shop Scheduling Problems,International Journal of Operational

Research, (in press) Vehicle routing problem (in progress)

Hybrid PSO GA for MRCPSP


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Hybrid PSO-GA for MRCPSP

Serial schedule method

Rank Chromosomes

Feasible schedule

A swarm of particles

A population ofchromosomes

Moregeneration ?

Crossover and mutationoperators

Selection operator

Update particles

Rank particles

More Iteration ? Stop No

Yes

No

Yes

Inner Loop

Particle - Chromosome Pair

Summary


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Summary

Multiple social structure PSO Measurement indices Heterogeneous particles Hierarchical PSO Successful applications to the following

combinatorial optimization problems JSP CVRP MRCPSP


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210 pso its eng apps

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